Simplify sin(30)cos(60)+sin(60)cos(30)

Problem

sin(30)*cos(60)+sin(60)*cos(30)

Solution

1. Identify the expression as a specific trigonometric identity. The expression follows the form sin(A)*cos(B)+cos(A)*sin(B)

2. Apply the formula for the sine of a sum, which states sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

3. Substitute the values A=30 and B=60 into the identity.

sin(30+60)

4. Add the angles inside the function.

sin(90)

5. Evaluate the sine of 90 using the unit circle or known trigonometric values.

sin(90)=1

Final Answer

sin(30)*cos(60)+sin(60)*cos(30)=1

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